Novel aspects of discrete dynamical type inequalities within fractional operators having generalized ℏ-discrete Mittag-Leffler kernels and application

Saima Rashid, Sobia Sultana, Zakia Hammouch, Fahd Jarad and Y.S. Hamed

Chaos, Solitons & Fractals, 2021, vol. 151, issue C

Abstract: Discrete fractional calculus (DFC) has had significant advances in the last few decades, being successfully employed in the time scale domain ℏZ. Understanding of DFC has demonstrated a valuable improvement in neural networks and modeling in other terrains. In the context of Riemann form (ABR), we discuss the discrete fractional operator influencing discrete Atangana-Baleanu (AB)-fractional operator having ℏ-discrete generalized Mittag-Leffler kernels. In the approach being presented, some new Pólya-Szegö and Chebyshev type inequalities introduced within discrete AB-fractional operators having ℏ-discrete generalized Mittag-Leffler kernels. By analyzing discrete AB-fractional operators in the time scale domain Z, we can perform a comparison basis for notable outcomes derived from the aforesaid operators. This type of discretization generates novel outcomes for synchronous functions. The specification of this proposed strategy simply demonstrates its efficiency, precision, and accessibility in terms of the methodology of qualitative approach of discrete fractional difference equation solutions, including its stability, consistency, and continual reliance on the initial value for the solutions of many fractional difference equation initial value problems. The repercussions of the discrete AB-fractional operators can depict new presentations for various particular cases. Finally, applications concerning bounding mappings are also illustrated.

Keywords: Discrete fractional calculus; Atangana-Baleanu fractional differences and sums; Discrete Mittag-Leffler function; Pólya-Szegö type inequality; Chebyshev inequality (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921005580

DOI: 10.1016/j.chaos.2021.111204

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